def shortest_paths(graph, start):
# Dijkstra's algorithm for single source shortest paths
# O(|V| log |V| + |E| log |V|)
paths = {node: None for node in graph}
distances = {node: float('inf') for node in graph}
distances[start] = 0
pq = PriorityQueue()
for node in graph:
if node == start:
pq.put(node, 0)
else:
pq.put(node, float('inf'))
while not pq.is_empty():
node, distance = pq.get()
for neighbour, edge_cost in graph[node]:
new_cost = distance + edge_cost
if new_cost < distances[neighbour]:
distances[neighbour] = new_cost
paths[neighbour] = node
pq.update(neighbour, new_cost)
return paths, distances
def shortest_paths(graph, start):
# Dijkstra's algorithm for single source shortest paths
# O(|V| log |V| + |E| log |V|)
paths = {node: None for node in graph}
distances = {node: float("inf") for node in graph}
distances[start] = 0
pq = PriorityQueue()
for node in graph:
if node == start:
pq.put(node, 0)
else:
pq.put(node, float("inf"))
while not pq.is_empty():
node, distance = pq.get()
for neighbour, edge_cost in graph[node]:
new_cost = distance + edge_cost
if new_cost < distances[neighbour]:
distances[neighbour] = new_cost
paths[neighbour] = node
pq.update(neighbour, new_cost)
return paths, distances
def setUp(self):
self.pq = PriorityQueue()
class TestPriorityQueue(unittest.TestCase):
def setUp(self):
self.pq = PriorityQueue()
def test_constructor(self):
self.assertTrue(self.pq.is_empty())
self.assertEquals(0, len(self.pq))
def test_one_put(self):
element = 'foo'
priority = 350
self.pq.put(element, priority)
self.assertFalse(self.pq.is_empty())
self.assertEquals(1, len(self.pq))
def test_multiple_put(self):
elements = range(100)
priority = 350
for element in elements:
self.pq.put(element, priority)
self.assertFalse(self.pq.is_empty())
self.assertEquals(len(elements), len(self.pq))
def test_one_get(self):
element = 'foo'
priority = 350
self.pq.put(element, priority)
self.assertEquals((element, priority), self.pq.get())
self.assertTrue(self.pq.is_empty())
self.assertEquals(0, len(self.pq))
def test_multiple_gets_sorted(self):
elements = string.lowercase
priorities = range(len(elements))
self._test_multiple_gets(elements, priorities)
def test_multiple_gets_sorted_reversed(self):
elements = string.lowercase
priorities = range(len(elements))[::-1]
self._test_multiple_gets(elements, priorities)
def test_multiple_gets_random(self):
trials = 10
elements = string.lowercase
priorities = range(len(elements))
for _ in range(trials):
random.shuffle(priorities)
self._test_multiple_gets(elements, priorities)
def test_get_empty(self):
self.assertRaises(IndexError, self.pq.get)
def test_get_too_many(self):
self.pq.put('foo', 350)
self.pq.get()
self.assertRaises(IndexError, self.pq.get)
def _test_multiple_gets(self, elements, priorities):
expected_gets = sorted(zip(elements, priorities),
key=operator.itemgetter(1))
for element, priority in zip(elements, priorities):
self.pq.put(element, priority)
for element, priority in expected_gets:
self.assertEquals((element, priority), self.pq.get())
self.assertTrue(self.pq.is_empty())
self.assertEquals(0, len(self.pq))
def setUp(self):
self.pq = PriorityQueue()
class TestPriorityQueue(unittest.TestCase):
def setUp(self):
self.pq = PriorityQueue()
def test_constructor(self):
self.assertTrue(self.pq.is_empty())
self.assertEquals(0, len(self.pq))
def test_one_put(self):
element = 'foo'
priority = 350
self.pq.put(element, priority)
self.assertFalse(self.pq.is_empty())
self.assertEquals(1, len(self.pq))
def test_multiple_put(self):
elements = range(100)
priority = 350
for element in elements:
self.pq.put(element, priority)
self.assertFalse(self.pq.is_empty())
self.assertEquals(len(elements), len(self.pq))
def test_one_get(self):
element = 'foo'
priority = 350
self.pq.put(element, priority)
self.assertEquals((element, priority), self.pq.get())
self.assertTrue(self.pq.is_empty())
self.assertEquals(0, len(self.pq))
def test_multiple_gets_sorted(self):
elements = string.lowercase
priorities = range(len(elements))
self._test_multiple_gets(elements, priorities)
def test_multiple_gets_sorted_reversed(self):
elements = string.lowercase
priorities = range(len(elements))[::-1]
self._test_multiple_gets(elements, priorities)
def test_multiple_gets_random(self):
trials = 10
elements = string.lowercase
priorities = range(len(elements))
for _ in range(trials):
random.shuffle(priorities)
self._test_multiple_gets(elements, priorities)
def test_get_empty(self):
self.assertRaises(IndexError, self.pq.get)
def test_get_too_many(self):
self.pq.put('foo', 350)
self.pq.get()
self.assertRaises(IndexError, self.pq.get)
def _test_multiple_gets(self, elements, priorities):
expected_gets = sorted(zip(elements, priorities),
key=operator.itemgetter(1))
for element, priority in zip(elements, priorities):
self.pq.put(element, priority)
for element, priority in expected_gets:
self.assertEquals((element, priority), self.pq.get())
self.assertTrue(self.pq.is_empty())
self.assertEquals(0, len(self.pq))